Decay of solutions to parabolic-type problem with distributed order Caputo derivative

Abstract

We consider the decay of solution to fractional diffusion equation with the distributed order Caputo derivative. We assume that the elliptic operator is time-dependent and that the weight function contained in the definition of the distributed order Caputo derivative is just integrable. We establish the relation between behavior of weight function near zero and the decay rate of solution.

References in corpus (2)

• Initial-boundary value problems for fractional diffusion equations with time-dependent coeffcients
• Initial-boundary value problem for distributed order time-fractional diffusion equations

Cited by in corpus (2)

• Well-posedness and asymptotic estimate for a diffusion equation with time-fractional derivative
• Sharp decay estimates and numerical analysis for weakly coupled systems of two subdiffusion equations